Fail Gafarov

Possibility between earthquake and explosion seismogram differentiation by discrete stochastic non-Markov processes and local Hurst exponent analysis

The basic scientific point of this paper is to draw the attention of researchers to new possibilities of differentiation of similar signals having different nature. One example of such kinds of signals is presented by seismograms containing recordings of earthquakes (EQs) and technogenic explosions (TEs). EQs are among the most dramatic phenomena in nature. We propose here a discrete stochastic model for possible solution of a problem of strong EQ forecasting and differentiation of TEs from the weak EQs. Theoretical analysis is performed by two independent methods: by using statistical theory of discrete non-Markov stochastic processes [Phys. Rev. E 62, 6178 (2000)] and the local Hurst exponent. The following Earth states have been considered among them: before (Ib) and during (I) strong EQ, during weak EQ (II) and during TE (III), and in a calm state of Earths core (IV). The estimation of states I, II, and III has been made on the particular examples of Turkey (1999) EQs, state IV has been taken as an example of Earths state before underground TE. Time recordings of seismic signals of the first four dynamic orthogonal collective variables, six various planes of phase portrait of four-dimensional phase space of orthogonal variables and the local Hurst exponent have been calculated for the dynamic analysis of states of systems I-IV. The analysis of statistical properties of seismic time series I-IV has been realized with the help of a set of discrete time-dependent functions (time correlation function and first three memory functions), their power spectra, and the first three points in the statistical spectrum of non-Markovity parameters. In all systems studied we have found a bizarre combination of the following spectral characteristics: the fractal frequency spectra adjustable by phenomena of usual and restricted self-organized criticality, spectra of white and color noises and unusual alternation of Markov and non-Markov effects of long-range memory, detected earlier [J. Phys. A 27, 5363 (1994)] only for hydrodynamic systems. Our research demonstrates that discrete non-Markov stochastic processes and long-range memory effects play a crucial role in the behavior of seismic systems I-IV. The approaches, permitting us to obtain an algorithm of strong EQ forecasting and to differentiate TEs from weak EQs, have been developed.

Stratification of the phase clouds and statistical effects of the non-Markovity in chaotic time series of human gait for healthy people and Parkinson patients

In this work we develop a new method of diagnosing the nervous system diseases and a new approach in studying human gait dynamics with the help of the theory of discrete non-Markov random processes (Phys. Rev. E 62 (5) (2000) 6178, Phys. Rev. E 64 (2001) 066132, Phys. Rev. E 65 (2002) 046107, Physica A 303 (2002) 427). The stratification of the phase clouds and the statistical non-Markov effects in the time series of the dynamics of human gait are considered. We carried out the comparative analysis of the data of four age groups of healthy people: children (from 3 to 10 year olds), teenagers (from 11 to 14 year olds), young people (from 21 up to 29 year olds), elderly persons (from 71 to 77 year olds) and Parkinson patients. The full data set are analyzed with the help of the phase portraits of the four dynamic variables, the power spectra of the initial time correlation function and the memory functions of junior orders, the three first points in the spectra of the statistical non-Markov parameter. The received results allow to define the predisposition of the probationers to deflections in the central nervous system caused by Parkinsons disease. We have found out distinct differences between the five submitted groups. On this basis we offer a new method of diagnostics and forecasting Parkinsons disease.

Intensity approximation of random fluctuation in complex systems

The Markov and non-Markov processes in complex systems are examined with the help of dynamical information Shannon entropy method. Here we consider the essential role of two mutually independent channels of entropy involving creation of correlation and annihilation of correlation. The developed method has been used to analyze the intensity fluctuation of the complex systems of various nature: in psychology (to analyze numerical and pattern short-time human memory, to study the effect of stress on the parameters of the dynamical taping-test) and in cardiology (to analyze the random dynamics of RR-intervals in human ECGs and to diagnose various diseases of human cardiovascular systems). The received results show that the application of intensity approximation allows to improve essentially the diagnostics of parameters in the evolution of human dynamic states.

Non-Markov stochastic dynamics of real epidemic process of respiratory infections

The study of social networks and especially of stochastic dynamics of diseases spread in human population has recently attracted considerable attention in statistical physics. In this work we present a new statistical method of analyzing the spread of epidemic processes of grippe and acute respiratory track infections (ARTI) by means of the theory of discrete non-Markov stochastic processes. We use the results of our last theory (Phys. Rev. E 65 (2002) 046107) to study statistical memory effects, long-range correlation and discreteness in real data series, describing the epidemic dynamics of human ARTI infections and grippe. We have carried out the comparative analysis of the data of the two infections (grippe and ARTI) in one of the industrial districts of Kazan, one of the largest cities of Russia. The experimental data are analyzed by the power spectra of the initial time correlation function and the memory functions of junior orders, the phase portraits of the four first dynamic variables, the three first points of the statistical non-Markov parameter and the locally averaged kinetic and relaxation parameters. The received results give an opportunity to provide a strict quantitative description of regular and stochastic components in epidemic dynamics of social networks taking into account their time discreteness and effects of statistical memory. They also allow to reveal the degree of randomness and predictability of the real epidemic process in the specific social network.

Long-range memory and non-Markov statistical effects in human sensorimotor coordination

In this paper, the non-Markov statistical processes and long-range memory effects in human sensorimotor coordination are investigated. The theoretical basis of this study is the statistical theory of non-stationary discrete non-Markov processes in complex systems (Phys. Rev. E 62, 6178 (2000)). The human sensorimotor coordination was experimentally studied by means of standard dynamical tapping test on the group of 32 young peoples with tap numbers up to 400. This test was carried out separately for the right and the left hand according to the degree of domination of each brain hemisphere. The numerical analysis of the experimental results was made with the help of power spectra of the initial time correlation function, the memory functions of low orders and the first three points of the statistical spectrum of non-Markovity parameter. Our observations demonstrate, that with the regard to results of the standard dynamic tapping-test it is possible to divide all examinees into five different dynamic types. We have introduced the conflict coefficient to estimate quantitatively the order-disorder effects underlying life systems. The last one reflects the existence of disbalance between the nervous and the motor human coordination. The suggested classification of the neurophysiological activity represents the dynamic generalization of the well-known neuropsychological types and provides the new approach in a modern neuropsychology.

Fluctuations and Noise in Stochastic Spread of Respiratory Infection Epidemics in Social Networks

For the analysis of epidemic and disease dynamics complexity, it is necessary to understand the basic principles and notions of its spreading in long‐time memory media. Here we considering the problem from a theoretical and practical viewpoint, presenting the quantitative evidence confirming the existence of stochastic long‐range memory and robust chaos in a real time series of respiratory infections of human upper respiratory track. In this work we present a new statistical method of analyzing the spread of grippe and acute respiratory track infections epidemic process of human upper respiratory track by means of the theory of discrete non‐Markov stochastic processes. We use the results of our recent theory (Phys. Rev. E 65, 046107 (2002)) for the study of statistical effects of memory in real data series, describing the epidemic dynamics of human acute respiratory track infections and grippe. The obtained results testify to an opportunity of the strict quantitative description of the regular and stochas...

Markov and non-Markov processes in complex systems by the dynamical information entropy

We consider the Markov and non-Markov processes in complex systems by the dynamical information Shannon entropy (DISE) method. The influence and important role of the two mutually dependent channels of entropy alternation (creation or generation of correlation) and anti-correlation (destroying or annihilation of correlation) have been discussed. The developed method has been used for the analysis of the complex systems of various natures: slow neutron scattering in liquid cesium, psychology (short-time numeral and pattern human memory and effect of stress on the dynamical taping-test), random dynamics of RR-intervals in human ECG (problem of diagnosis of various disease of the human cardio-vascular systems), chaotic dynamics of the parameters of financial markets and ecological systems.